# ############################################################################ # (c) Chancellery of the Prime Minister 2012-2015 # # # # Authors: Grzegorz Klima, Karol Podemski, Kaja Retkiewicz-Wijtiwiak # # ############################################################################ # Two-country model with perfect risk sharing (formulated using templates) # ############################################################################ options { output logfile = TRUE; output LaTeX = TRUE; output LaTeX landscape = TRUE; }; indexsets { COUNTRY = { 'H', 'F' }; }; tryreduce { pi<'H'>[], pi<'F'>[], PI<'F'>[], PI<'H'>[], T<'H'>[], K_d<'H'>[], H_d<'H'>[], T<'F'>[], K_d<'F'>[], H_d<'F'>[], TR<'F'>[]; }; block CONSUMER { definitions { u[] = (C[]^(mu) * (1 - H[])^ (1 - mu)) ^ (1 - eta) / (1 - eta); }; controls { K[], C[], H[], I[]; }; objective { U[] = u[] + beta * E[][U[1]]; }; constraints { I[] + C[] + T[] = pi[] + r[] * K[-1] + W[] * H[] - psi * K[-1] * (I[] / K[-1] - delta) ^ 2 + TR[] : lambda_c[]; K[] = (1 - delta) * K[-1] + I[]; }; }; block FIRM { controls { K_d[], H_d[], Y[], pi[]; }; objective { PI[] = pi[]; }; constraints { Y[] = Z[] * K_d[] ^ alpha * H_d[]^(1 - alpha); pi[] = Y[] - H_d[] * W[] - r[] * K_d[]; }; }; block EQUILIBRIUM { identities { SUM(TR[]) = 0; K_d[] = K[-1]; H_d[] = H[]; T[] = G_d[]; lambda_c<'H'>[] = lambda_c<'F'>[]; # Risk sharing condition }; }; block EXOG { identities { G_d[] = (phi_G * (G_d[-1]) + epsilon_G[]); Z[] = exp(phi_Z * log(Z[-1]) + epsilon_Z[]); }; shocks { epsilon_G[], epsilon_Z[]; }; };